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近年来, 图像加密技术备受关注. 随着人们对通信隐私及网络安全重视程度的提高, 对信息加密技术的要求更加严格, 图像作为信息的载体之一, 因携带信息的有效性和生动性而受到重视. 本文提出一种基于DNA编码与交替量子随机行走的彩色图像加密算法. 量子随机行走作为出色的密码学工具参与算法流程中各个部分, DNA编码作为核心加密方式完成算法. 本文详细描述加密、解密流程, 并对所提出算法进行仿真实验验证与结果分析. 仿真阶段设计模拟密钥参数, 编码进行彩色图像加密、解密实验, 并进行了相关分析. 实验结果表明, 本文提出的彩色图像加密算法能够进行安全有效的彩色图像加密, 且相关分析表示其加密后图像直方图平稳、像素相关性系数趋近于0、密钥空间
${2^{ 128}} $ , 三通道信息熵达到7.997以上, 能够抵御统计攻击、穷举攻击等攻击手段. 此外, DNA编码除新颖的编码及运算方式之外还有其独特的生物学特性, 为密码学的研究提供了新的思路与方向.In recent years, image encryption technology has attracted much attention. As people pay more attention to communication privacy and network security, the requirements for information encryption technology are more stringent. As one of the information carriers, images are valuable for carrying the effectiveness and vividness of the information. This paper proposes a color image encryption algorithm based on DNA encoding and alternating quantum random walk. Quantum random walk is an excellent cryptographic tool that participates in all parts of the algorithm process, and DNA encoding is used as the core encryption method to complete the algorithm. This article describes the encryption and decryption process in detail, and conducts simulation experiments to verify and analyze the results of the proposed algorithm. In the simulation stage, we design the simulation key parameters, encode the color image encryption and decryption experiments, and carry out related analysis. The experimental results show that the color image encryption algorithm proposed in this paper can perform safe and effective color image encryption. The correlation analysis shows that the image histogram after encryption is stable, the pixel correlation coefficient approaches 0, and the key space is${2^{ 128 }} $ , the three-channel information entropy reaches more than 7.997, which can resist statistical attacks, brute force attacks and other attack methods. In addition, DNA coding has unique biological characteristics in addition to the novel coding and calculation methods, which provide new ideas and directions for cryptographic research.-
Keywords:
- quantum information /
- quantum random walk /
- image encryption /
- DNA coding
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图 1 双方向格点上交替量子随机行走
Fig. 1. Alternating quantum random walking on the bidirectional grid.
图 4 Lena图像加密前后相关性分析
Fig. 4. Correlation analysis of images before and after Lena encryption.
图 6 小猫图像加密前后相关性分析
Fig. 6. Correlation analysis of images before and after cat encryption.
图 5 蛋糕图像加密前后相关性分析
Fig. 5. Correlation analysis of images before and after cake encryption.
图 7 Lena图像加密前后三通道直方图分析
Fig. 7. Analysis of R, G, B three-channel histogram before and after lena image encryption.
表 1 8种DNA编码方案
Table 1. Eight DNA coding schemes.
1 2 3 4 5 6 7 8 A 00 00 01 01 10 10 11 11 G 01 10 00 11 00 11 01 10 C 10 01 11 00 11 00 10 01 T 11 11 10 10 01 01 00 00 注: 满足DNA的生物学特性A-T互补、G-C互补. 
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表 2 DNA编码方案1对应的加法方案1
Table 2. Addition plan 1 corresponding to DNA coding plan 1.
+ A G C T A A G C T G G C T A C C T A G T T A G C
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表 3 DNA编码方案1对应的减法方案1
Table 3. DNA coding scheme 1 corresponding to subtraction scheme 1.
– A G C T A A G C T G T A G C C C T A G T G C T A
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表 4 像素相关性分析数据
Table 4. Pixel correlation analysis data.
图像 方向 数值 原始图像 加密图像 Lena 水平 0.9275 0.0017 垂直 0.9603 –0.0005 对角 0.8941 0.0007 小猫 水平 0.9429 0.0026 垂直 0.9377 0.0009 对角 0.9097 –0.0012 蛋糕 水平 0.9229 0.0076 垂直 0.9056 0.0017 对角 0.8647 0.0017
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表 6 密钥敏感性分析数据
Table 6. Key sensitivity analysis data.
图像 通道 NPCR UACI Lena Red 99.6040% 33.4005% Green 99.6195% 33.2311% Blue 99.5826% 33.5902% 小猫 Red 99.6326% 33.6785% Green 99.6124% 33.4455% Blue 99.6147% 33.5784% 蛋糕 Red 99.6124% 33.4461% Green 99.6528% 33.5315% Blue 99.7004% 33.4499%
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[1] Zheng R H, Xiao Y, Su S L, Chen Y H, Shi Z C, Song J, Xia Y, Zheng S B 2021 Phys. Rev. A 103 052402
Google Scholar
[2] Kang Y H, Shi Z C, Huang B H, Song J, Xia Y 2020 Phys. Rev. A 101 032322
Google Scholar
[3] Long G L 2001 Phys. Rev. A 64 022307
Google Scholar
[4] Long G L, Li X, Sun Y 2002 Phys. Lett. A 294 143
Google Scholar
[5] Li T, Zhang S, Fu X Q, Wang X, Wang Y, Lin J, Bao W S 2019 Chin. Phys. B 28 120301
Google Scholar
[6] Liu F, Zhang X, Xu P A, He Z X, Ma H Y 2020 Int. J. Theor. Phys. 59 3491
Google Scholar
[7] Zhou N R, Li J F, Yu Z B, Gong L H, A Farouk 2017 Quantum Inf. Process. 16 1
Google Scholar
[8] Gong L H, Li J F, Zhou N R 2018 Laser Phys. Lett. 15 105204
Google Scholar
[9] Hu X M, Huang C X, Sheng Y B, Zhou L, Liu B H, Guo Y, Zhang C, Xing W B, Huang Y F, Li C F, Guo G C 2021 Phys. Rev. Lett. 126 010503
Google Scholar
[10] Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12
Google Scholar
[11] Yan Z H, Qin J L, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2021 Fundam. Res. 1 43
Google Scholar
[12] Zhao J B, Zhang W B, Ma Y L, Zhang X H, Ma H Y 2020 Appl. Sci. 10 1935
Google Scholar
[13] Qiu T H, Li H, Xie M, Liu Q, Ma H Y 2019 Opt. Express 27 27477
Google Scholar
[14] Ma H Y, Xu P A, Shao C H, Chen L B, Li J X, Pan Q 2019 Int. J. Theor. Phys. 58 4241
Google Scholar
[15] Li H S, Fan P, Xia H Y, Peng H L, Long G L 2020 Sci. China Phys. Mech. 63 1
[16] Zheng R H, Kang Y H, Su S L, Song J, Xia Y 2020 Phys. Rev. A 102 012609
Google Scholar
[17] Ma H Y, He Z X, Xu P A, Dong Y M, Fan X K 2020 Quantum Inf. Process 19 1
[18] Xu P A, He Z X, Qiu T H, Ma H Y 2020 Opt. Express 28 12508
Google Scholar
[19] Zhou N R, Huang L X, Gong L H, Zheng Q W 2020 Quantum Inf. Process. 19 1
[20] Li H S, Fan P, Xia H Y, Peng H L, Long G L 2020 Sci. China. Phys. Mech. 63 1
[21] Castagnoli G 2016 Found Phys. 46 360
Google Scholar
[22] Castagnoli G 2016 Quanta 5 34
Google Scholar
[23] Gong L H, Song H C, He C S, Liu Y, Zhou N R 2014 Phys. Scr. 89 035101
Google Scholar
[24] Li H H, Gong L H, Zhou N R 2020 Chin. Phys. B 29 110304
Google Scholar
[25] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 48 1687
Google Scholar
[26] Farhi E, Gutmann S 1998 Phys. Rev. A 58 915
Google Scholar
[27] Watrous J 2001 Comput. Syst. Sci. 62 376
Google Scholar
[28] Abd El-Latif A A, Abd-El-Atty B, Venegas-Andraca S E, Elwahsh H, Piran M J, Bashir A K, Song O, Mazurczyk W 2020 IEEE Access 8 92687
Google Scholar
[29] Abd-El-Atty B, Iliyasu A M, Alaskar H, Abd El-Latif A A 2020 Sensors 20 3108
Google Scholar
[30] Abd EL-Latif A A, Abd-El-Atty B, Venegas-Andraca S E 2020 Physica A 547 123869
Google Scholar
[31] Abd El-Latif A A, Abd-El-Atty B, Elseuofi S, Khalifa H S, Alghamdi A S, Polat K, Amin M 2020 Physica A 541 123687
Google Scholar
[32] Abd-El-Atty B, Amin M, Iliyasu A M 2020 Sci. Rep. 10
[33] Godsil C, Zhan H 2019 J. Comb. Theory Ser. A 167 181
Google Scholar
[34] Abd-El-Atty B, Iliyasu A M, Alanezi A, Abd EL-Latif A A 2021 Opt. Lasers Eng. 138 106403
Google Scholar
[35] Adleman L M 1994 Science 266 1021
Google Scholar
[36] Leier A, Richter C, Banzhaf W, Rauhe H 2000 Biosystems 57 13
Google Scholar
[37] Chen J 2003 Proceedings of the 2003 International Symposium on Circuits and Systems ISCAS'03. IEEE 2003 3 III-III.
[38] Chang W L, Guo M, Ho M S H 2005 IEEE Trans Nanobiosci. 4 149
Google Scholar
[39] Lu M X, Lai X J, Xiao G Z, Qin L 2007 Sci. China Inf. Sci. 50 324
Google Scholar
[40] Lai X J, Lu M X, Qin L, Han J S, Fang X W 2010 Sci. China Inf. Sci. 53 506
Google Scholar
[41] Wei X, Guo L, Zhang Q, Zhang J, Lian S G 2012 J. Syst. Softw. 85 290
Google Scholar
[42] Niu Y, Zhang X, Han F 2017 Comput. Intell. Neurosci. 2017
[43] Kalsi S, Kaur H, Chang V 2018 J. Med. Syst. 42 1
Google Scholar
[44] Basu S, Karuppiah M, Nasipuri M, Halder A K, Radhakrishnan 2019 J. Syst. Archit. 94 24
Google Scholar
[45] Biswas M R, Alam K M R, Tamura S, Morimoto Y 2019 J. Syst. Archit. 48 102363
[46] Huang L, Wang S, Xiang J, Sun Y 2020 Math. Prob. Eng. 2020
[47] Alghafis A, Firdousi F, Khan M, Batool A L, Amin M 2020 Math. Comput. Simul. 177 441
Google Scholar
[48] Eswaran P, Shankar K 2017 Int. J. Pure Appl. Math. 118 393
[49] Lu Q, Zhu C, Deng X 2020 IEEE Access 8 25664
Google Scholar
[50] Wang Y, Ye S C, Wang Y 2020 Microelectron. Comput. 37 71
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